Internal problem ID [3839]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 589.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 x^{4} y y^{\prime }+2 x^{3} y^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(3*x^4*y(x)*diff(y(x),x) = 1-2*x^3*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 c_{1} x^{3}\right )}}{5 x^{\frac {13}{3}}} y \left (x \right ) = \frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 c_{1} x^{3}\right )}}{5 x^{\frac {13}{3}}} \end{align*}
✓ Solution by Mathematica
Time used: 3.675 (sec). Leaf size: 51
DSolve[3 x^4 y[x] y'[x]==1-2 x^3 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} y(x)\to \sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \end{align*}